Abstract
We prove constructively (in the style of Bishop) that every monotone continuous function with a uniform modulus of increase has a continuous inverse. The proof is formalized, and a realizing term extracted. This term can be applied to concrete continuous functions and arguments, and then normalized to a rational approximation of say a zero of a given function. It turns out that even in the logical term language “normalization by evaluation” is reasonably efficient.
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Schwichtenberg, H. (2006). Inverting Monotone Continuous Functions in Constructive Analysis. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_50
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DOI: https://doi.org/10.1007/11780342_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35466-6
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